Question $1$

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Now that she has accumulated a deposit of $$300,000,$ Wendy wishes to use this deposit and take out a housing loan to purchase a home. The home costs $$900,000.$ The loan is to be repaid in equal quarterly instalments over a term of $15$ years. Wendy recalls that the interest rate quoted by the bank is an annual nominal rate of $4\mathrm{.}2\%$pa compounded quarterly. After $5$ years $(20$th repayment just about to be made$),$ Wendy gets a large bonus at work and decides to pay out what is owing on the loan.

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$($i$)$ How much is the quarterly repayment?

$($ii$)$ How much is owed at the time of the pay out?

$($iii$)$ Provide Wendy with a repayment schedule using excel at the time the loan is made.

$($Answers should be accurate to the nearest dollar$)$